The Hyperbolic Vacuum: A Zero-Parameter Cosmology and an Exact Solution of Einstein's Field Equations

The spacetime interval ds² = c²dt² − dr² describes a universe of negatively curved (hyperbolic) geometry and is itself an exact vacuum solution of Einstein's field equations, with k = −1, ρ = 0, Λ = 0, and a(t) = ct. Taken at face value as the expansion history of the universe after recombination — everything scoped to z < 100, with the earlier universe neither modelled nor claimed — it yields a cosmology with no free parameters except the age of the universe, which is well established by several methods independent of the cosmological model. From that single input the luminosity distance follows in closed form, d_L(z) = (c/H₀)(1+z)sinh(ln(1+z)) = (c/H₀)·z(1+z/2), and the Hubble constant from the age alone, H₀ = 71.9 ± 2.6 km/s/Mpc. With zero adjustable parameters and no dark energy the geometry reproduces the Type Ia supernova luminosity distances — Pantheon+ (χ²/dof = 0.910, 1580 supernovae) and the disjoint DES-SN5YR sample (χ²/dof = 0.888, 1623 supernovae). The concordance model appears to be a heuristic fit to the underlying hyperbolic spacetime, its two density parameters the coordinate freedom needed to express negative spatial curvature in flat-space language. Two direct measurements are reported: an effective-curvature channel Ω_zam = −0.03 ± 0.14, and a homogeneous matter component bounded at Ω_m ≤ 0.038 (95%) — below the known baryon density, consistent with matter residing in walls rather than as a homogeneous component. The framework predicts redshift drift identically zero, an algebraic identity H(z) = H₀(1+z), falsifiable within ELT-ANDES design sensitivity. The age–redshift identity t(z) = t₀/(1+z) gives high-redshift objects 2.6–3.4× more cosmic time to form than flat ΛCDM allows, dissolving the JWST "impossibly early galaxy" tension. The paper states plainly the three early-universe constraints the strict late-time geometry does not meet — the CMB acoustic angle, structure formation, and primordial nucleosynthesis — as explicit requirements on any completion rather than as solved problems. Standing open problems are stated with named tests: the DESI DR2 Alcock-Paczynski shape mismatch (χ² = 135.3/6 under ΛCDM-fiducial extraction) and a Pantheon+ residual of Δχ² = 49.6. A decision table commits in advance to which claims each scheduled measurement would kill. This is submitted as a solicitation: the decisive tests require collaboration-scale pipelines the author does not hold, and are specified precisely so that groups holding them can perform them.